Tuesday, August 30, 2005

To prevent comment spam, blogger setting now has one new option word verification. It is available in Settings --> Comments tab. Choose yes for Show word verification for comments. People who leave comments will be asked to write a random word shown as an image. This will prevent automated systems from leaving comment spams. The blogger help is here.

I have chosen this option. I hope those who like to leave comments would not feel this as a burden. A small inconvenience to keep the comments clean. Thanks to Mogadalai who informed me about this option.

Saturday, August 27, 2005

Krantz has written a book on problem solving, a book on mathematical writing, and another on teaching mathematics. All of them are worth reading. I read "How to teach mathematics - A personal perspective" a long time ago. Here are the notes that I wrote down while reading the book. I am publishing them in this blog to give a flavour of the book, and to indicate that hunting this book down might be worth the effort.---------------------------------------------------------------------------------------

You cannot learn to play piano or to ski by watching someone else do it.

And the fact that having sat in a classroom for most of your life does not mean that you know how to teach.

Teaching is important.

The good news is that it requires no more effort, no more preparation, and no more time to be a good teacher than to be a bad teacher.

As with any endeavour that is worth doing well, teaching is one that will improve if it is subjected to periodic re-examination.

There are some things that we do not learn by osmosis. How to lecture and how to teach are among these.

After all, teaching is a rather personal activity.

Picasso's revolutionary techniques in painting were based on solid classical foundation. By analogy, I think that before you consider new teaching techniques you should acquaint yourself with the traditional ones.

You cannot be a good teacher if you do not respect yourself.

a] Dress appropriately for the occasionb] Make an effort to communicate with your audiencec] Respect the point of view of the audience

Have your materials completely mastered before you enter the classroom.

To me, preparation is the core of teaching.

Treat the questions with respect.

Students will rise to a challenge, provided the teacher starts with small challenges ad works up to big ones.

There is something of value, of an intangible nature, about passing knowledge along to other people.

I have long felt that those who cannot teach are those who do not care about teaching.

Prepare, be organized, be fair, be receptive to questions, meet your office hours, and so forth.

Do not introduce distractions into the classroom atmosphere.

The attitude in your class should be that you and the students are working together to conquer the material.

Be comfortable with your class.

Be willing to try new things.

Over preparation will make you lose your spontaneity.

You cannot learn to play the piano by accident.

Teaching is a yoga. Your mantra is "am I getting through to them?"

One of Mozart's most effective tools in his compositions was to repeat a particularly beautiful passage. We can benefit from his example.

A teacher foes not just lecture and answer questions. A good teacher helps students to discover the ideas. There are a few things more stimulating and rewarding than a class in which the students are anticipating the ideas because of seeds that you have planted. The way that you construct your lecture and your course is one device for planting those seeds. The way that you answer questions is another.

"There is no substitute to knowing what you are talking about"--Jonathan RT Hughes, Professor of Economic History

Mathematics can be understood deductively from certain axioms but it is learnt inductively.

Go from the simple to the complex.

The easiest thing in the world for a mathematician to do is to state theorems and prove them. It requires more effort tot each.

It is my opinion that the very best students tend to teach themselves.

No methodology is perfect.

Write neatly.

Keep as much material as possible visible at all times.

Homework assignment should neither be long nor short. It should touch on all important aspects and should drill the students on the material that you want them to learn and the material on which you will be testing them. At least part of the homework should be graded. Exams should be based only on material given as homework.

Make sure that the questions you ask elicit the basic information that you seek.

You must personally work the test out completely before you give it to your class.

An exam that needs you 10 to 15 minutes is ideal for a 50 minutes test.

Make the student read your solution before you agree to talk about grading the problem.

A good math student must be self-motivated.

It is a strange facet of the human condition that most of us don't know consciously what we think about most of the things most of the time.

An extreme example of a teaching style that is virtually orthogonal to what we Americans know is the one that has been attributed to the celebrated Hungarian analyst F. Riesz. He would come to class accompanied by an Assistant Professor and an Associate Professor. The Associate Professor would read Riesz's famous text aloud to the class. The Assistant Professor would write the words on the blackboard. Riesz would stand front and center with his hands clasped behind his back and nod sagely.

The famous mathematics teacher RL Moore is said to have once brought a Colt-45 to an unruly math class, set it conspicuously on the table, and then proceeded into his lecture in a room so quiet that one could have heard hair grow.

Thursday, August 11, 2005

There have been quite a few announcements, from Government of India, about science committees and the importance of research initiatives to launch the country into the Global Knowledge Orbit is also stressed again and again by the Prime Minister and others.

...Thus even prima facie, it seems that this round of proposals and announcements has a substantially ad hoc character leading one to doubt whether they indeed amount to a serious initiative to re-vitalise research in the basic sciences. But the manner in which these initiatives are fashioned and announced points to a deeper malaise in the formulation of science policy in this country.

The policy and decision-making process in Indian science rests on a small and narrow base that has very little input from the vast majority of productive and working scientists in the country. Policy-making in India is the exclusive province of a few eminent scientists, the secretaries of major scientific departments, the directors of some major scientific institutions and a few other members of the scientific bureaucracy...

Wednesday, August 10, 2005

Steven G Krantz is a Professor of mathematics with a flair for writing. I love his writing style. Here are a few typical examples of the language that Krantz uses in his writing. The first is from his review of "The man who loved only numbers" and "My brain is open" published in The College Mathematics Journal (Vol. 32, No. 3, May 2001). The second and third are from his review of the book A new kind of science authored by Stephan Wolfram - The complete review may be be found at the following URL: http://www.math.wustl.edu/~sk/.

(1) A recent Monthly review of these two books concludes by saying that Hoffman's book is for the masses while Schechter's is for fellow mathematicians and physicists. This may be a polite way of saying that Hoffman's book is careless while Schechter's is a cogent and planned effort. Schechter can be held accountable; Hoffman cannot.

(2) At the end of the film Chinatown, detective Jake Gittes (played by Jack Nicholson) has uncovered a vastly complex and nefarious web of evilperpetrated by wealthy land mogul Noah Cross (played by John Huston). In the dramatic closing scene, Nicholson is trying to find words to explain the police the infrastructure of depravity that he has identified; but he can find no way to articulate his thoughts. He ultimately points at Huston and cried, "He's rich!" Huston adopts a wry look on his face, smiles, and says, "I didn't know it was a crime to be rich...," and then credits roll. Stephen Wolfram seems to have uncovered a vastly complex and profound scheme of how the world functions. His intention is that his ideas will supersede all previous scientific thought--from Archimedes to Newton to Heisenberg to Witten. He has invested ten years and 1280 pages (and 100 million keystrokes on his computer!) in endeavouring to explain his discovery--not just to his colleagues but to the world at large. It is a noble effort, but in the end he is merely pointing his finger and crying, "It is complex!" I can just hear old Mother Nature saying, "I didn't know it was a crime to be complex."

(3) A number of years ago, the Dalai Lama visited the United States. As part of his travels, he visited the headquarters in Chicago of one of the great American news magazines. He was given the Cook's tour, and then there was a grand formal lunch at which the various executives of the enterprise pontificates ad nauseum. The Dalai Lama-an elfin man--sat swathed in his saffron robe, and inscrutable smile on his face, saying nothing. After about an hour, the CEO of the publishing company turned to the Dalai Lama and said, "Do you have any questions about our magazine, the nation's premiere news magazine? Go ahead, ask us anything at all." The Dalai Lama bowed his head for a moment, apparently deep in thought. Then he looked up and said, "Why do you publish it?"

Wednesday, August 03, 2005

The Prime minister of India, Manmohan Singh constituted the National Knowledge Commission two months ago. Media reported the news on June 02, 2005. He launched the Commission yesterday - August 02, 2005. The Commission is supposed to identify its action programme by October 02, 2005. Shall we expect something special on Gandhi Jayanthi day?

The key points in his speech are,

Public and private sectors are not able to cope with the demand for higher and professional education.

Universities and centers of excellence are falling behind the best in the world, both in terms of human capital and infrastructure.

India should be able to attract global investment in Reseach and Development (R&D) activities.

Putting in place the required legal and physical infrastructure that can attract more foreign investment in R&D activities in India.

Commission should come forward with ideas to promote the "knowledge base" of our economy.

Make the country truly the "knowledge engine" of the world.

Commission must come up with bold proposals to improve the excellence in research and teaching.

It is very difficult to avoid noticing that these ideas revolve around attracting foreign investment. The Prime minister said, in June, that the Commission has been constituted to prepare the country to meet knowledge challenges in the 21st century. He also remarked that the Commission will advise in knowledge production, knowledge use and knowledge dissemination. He now seemingly believes that country can face all those challenges with the help of foreign investment. It is not clear, as it is not reported in the media, if he has used the same slogans of production,use and dissemination during the launch. What about our Communist friends in the Commission? They must be thanking their stars for not having active labour unions in R&D sector as in manufacturing sectors!

Monday, August 01, 2005

The following passage is taken from Maxim Gorky'sMy Universities. My Universities is the third part of Gorky's autobiographical trilogy; the other two are My childhood and In the world. The latter part of this book describes his life in a village on the banks of Volga. Gorky's description of the village life is very poetic, and reminded me of RK Narayan and The Remembered Village of MN Srinivas. The present extracts come from the part where he describes his experiences in teaching an illiterate fisherman of the village to read and write, and how the fisherman Izot responds to his reading experience.

He was a very enthusiastic and fairly good pupil and would be absolutely amazed at his own progress. Sometimes, during a lesson, he would suddenly get up, take a book from the shelf, raise his eyebrows high and read two or three lines after a great effort. His face would turn red and he would look at me and say in an astonished voice: 'You see, I can read, ever hear anything like it!" Then he would close his eyes and repeat some poetry:

"Just like a mother mourning over the grave of her son,So wails the sandpiper over the desolate plain..."

'Read it?'

Several times he would ask cautiously, almost in a whisper: 'Tell me, my friend, how it all comes about. A man looks at these commas and hyphens and they turn into words and I recognize them, they're our living words! How do I know this? No one's whispering them into my ear. If these were pictures, then I could understand. But here it seems that the thoughts themselves are printed on the page - how do they do it?'

What could I answer? My 'don't know' annoyed him.

'The work of a magician!' he said sighing, as he peered at the pages and held them up to the light.

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